Exponential Stability of Nonlinear Fractional Stochastic System with Poisson Jumps

TL;DR

This paper investigates the exponential stability of nonlinear fractional stochastic systems with Poisson jumps, establishing conditions for stability and providing numerical examples to demonstrate the results' effectiveness.

Contribution

It introduces new stability criteria for nonlinear fractional stochastic systems with Poisson jumps using Mittag-Leffler functions and fixed point methods.

Findings

Established existence and uniqueness of solutions.

Proved exponential stability under certain conditions.

Validated results with a numerical example.

Abstract

In this paper exponential stability of nonlinear fractional order stochastic system with Poisson jumps is studied in finite dimensional space. Existence and uniqueness of solution, stability and exponential stability results are established by using boundedness properties of Mittag-Leffler matrix function, fixed point route and local assumptions on nonlinear terms. A numerical example is given to illustrate the efficiency of the obtained results. Finally, conclusion is drawn.